7. Find the second partial derivatives for f(x,y)-2x2y5y-3x2ya 8. Find the total differential for z -3ycosx+4x3уг. 9. Let w-xy-y3, x-In t, y-cos t. Use Chain Rule to find dw/dt when t-0. 10. Find dy/dx implicitly for y5-y43yx3-6-0. 11. Find a directional derivative for fíx,y)-2+y2 at (-2,3) in the direction 2 of u cos i sin-i. 12. Find the gradient for f(x,y)-x2y-x In y at (4,1).

Question

Solution for all

7. Find the second partial derivatives for f(x,y)-2x2y5y-3x2ya
8. Find the total differential for z -3ycosx+4x3уг.
9. Let w-xy-y3, x-In t, y-cos t. Use Chain Rule to find dw/dt when t-0.
10. Find dy/dx implicitly for y5-y43yx3-6-0.
11. Find a directional derivative for fíx,y)-2+y2 at (-2,3) in the direction
2
of u cos i sin-i.
12. Find the gradient for f(x,y)-x2y-x In y at (4,1).
Expand
Transcribed Image Text

7. Find the second partial derivatives for f(x,y)-2x2y5y-3x2ya 8. Find the total differential for z -3ycosx+4x3уг. 9. Let w-xy-y3, x-In t, y-cos t. Use Chain Rule to find dw/dt when t-0. 10. Find dy/dx implicitly for y5-y43yx3-6-0. 11. Find a directional derivative for fíx,y)-2+y2 at (-2,3) in the direction 2 of u cos i sin-i. 12. Find the gradient for f(x,y)-x2y-x In y at (4,1).

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